Distributed Approximate Distance Oracles.

Data structures that allow efficient distance estimation (distance oracles or distance sketches) have been extensively studied, and are particularly well studied in centralized models and classical distributed models such as the CONGEST model. We initiate their study in newer (and arguably more realistic) models of distributed computation such as the Congested Clique model and the Massively Parallel Computation (MPC) model, as well as in related big data models such as streaming and semi-streaming. We provide algorithms for constructing the well-known Thorup-Zwick distance oracle (or distance sketches) in multiple different computational models and discuss the tradeoffs between different complexity measures such as space, time, approximation ratio, and communication complexity.